MA 1170 Lecture 05 - Intro to Dierentiation
Friday, January 28, 2011
Objectives: Use limits to compute instantaneous speed/velocity exactly.
Instantaneous Speed and the derivative
From last time, we were dropping a rock o of a bridge 144 feet high, its he
MA 1170 Lecture 14 - Relative Maximums and Minimums
Friday, February 25, 2011
Objectives: Finding relative minimums and maximums
Consider the function
f(x) = x3 6x2 + 9x + 4.
(1)
Lets nd the critical points for this function. Remember that these occur whe
MA 1170 Lecture 12 - The Graph of the Derivative
Monday, February 21, 2011
Objectives: Using derivatives to analyze maximums and minimums.
Over the last several weeks, weve been going over dierentiation formulas, and we can take derivatives of
most of the
MA 1170 Lecture 15 - The Second Derivative Test
Wednesday, March 16, 2011
Objectives: Determining maxs and mins using the second derivative
Last time, we found critical points, and we could tell if a critical point is a relative maximum, relative
minimum,
MA 1170 Lecture 13 - Critical Points
Friday, February 25, 2011
Objectives: Review factoring easy quadratics. Introduce critical points.
Well be interested in nding where the derivative of a function is zero, and this will involve solving equations.
The wo
MA 1170 Lecture 09 - Product Rule
Monday, February 14, 2011
Objectives: The product rule.
The derivative rules weve had so far are relatively simple, but its important that we be very careful about
what we apply them to. As of now, we can dierentiate (tak
MA 1170 Lecture 11 - Chain Rule
Friday, February 18, 2011
Objectives: The chain rule.
The last of the major dierentiation rules is called the chain rule. It deals with the case, where one function
is put inside of another.
For example, given f(x) = x3 , w
MA 1170 Lecture 10 - Quotient Rule
Wednesday, February 16, 2011
Objectives: The quotient rule.
Last time, we saw the product rule. Very similar to it is something called the quotient rule. It goes like this.
Theorem 1. (The Quotient Rule) If
(1)
h(x) =
f
MA 1170 Lecture 07 - Some Dierentiation Formulas
Friday, February 4, 2011
Objectives: Motivate and use power rule (a dierentiation rule)
I will expect that you could reproduce the derivation of the derivative for f(x) = x2 . Im going to do the
same for f(
MA 1170 Lecture 08 - Sums and Contant Multiples
Friday, February 11, 2011
Objectives: The constant, sum and constant multiple rules.
I said that the power rule applies to all exponents other than zero. In some sense, the zero exponent is OK,
but we can al
MA 1170 Lecture 03 - Intro to Limits and Domains
Monday, January 24, 2011
Objectives: Introduce concept of limit and limit notation.
Limits
Generally, if we graph a function from its function rule, we get a nicely continuously curved graph. We can
think o
MA 1170 Lecture 06 - Graphical Interpretation of the Derivative
Monday, January 31, 2011
Objectives: Compare speed to slope.
Graphical interpretation of the derivative
It turns out that the computations weve been doing correspond to slopes, as in the slop
MA 1170 Lecture 02 - Intro to Limits and Domains
Friday, January 21, 2011
Objectives: Introduce preliminary concept of limit. Introduce the domain of a function.
Limits
The functions we generally come across tend to be extremely well-behaved in the sense
MA 1170 Lecture 04 - An Application of Limits
Wednesday, January 26th, 2011
Objectives: Use limits to compute instantaneous speed/velocity.
Speed
If you were to drop a rock o of a bridge 144 feet high, its approximate height would be given by the function
MA 1170 Lecture 01 - Function Notation and Graphs
Wednesday, January 19, 2010.
Objectives: Review function notation, graphing functions, and reading graphs.
Function notation
In algebra, you may have worked with equations in two variables, like
(1)
x 2y =